Theorem 11.1.52B3316345A4A

Proof. Expand $(\omega +\mathrm{dd}^{\mathrm{c}}u)^ n$ by the binomial theorem. The term with $k=n$ integrates to zero, since it is exact:

For $1\leq k\leq n-1$, apply lemma 11.1.2 with $f=u$ and $T=(\mathrm{dd}^{\mathrm{c}}u)^{k-1}\wedge \omega ^{n-k}$. Since both $\mathrm{d}$ and $\mathrm d^{\mathrm c}$ annihilate $\mathrm{dd}^{\mathrm{c}}u$,

which gives the $k$th term of (11.1.6). When $n=1$, the sum is empty and the mass is constant. $\square$